On bond failure by splitting of concrete cover surrounding anchored bars

This study develops analytical expressions for the bond stress level surrounding a longitudinal steel bar that causes the cover concrete to fail in a splitting mode, with bar-to-surface cracks forming in the longitudinal direction parallel to the bar. The proposed models use as a foundation the fracture mechanicsbased cohesive-elastic ring model, developed by Reinhardt&Van der Veen (1990) based on original work by Tepfers (1979). They propose formulations that better address the assumptions and simplifications made in the original model, namely the biaxial behavior of concrete in tension, the crack-opening displacement profile, and the material law governing post-cracking tension softening. The relative significance of the proposed model enhancements is established through their prediction of bond stress and the associated computational cost for a computational benchmark problem involving a steel bar pullout from a concrete cylinder. Finally, the robustness of the reference and proposed models, measured by their sensitivity to the uncertainty in their respective parameters is evaluated and compared using a deterministic sensitivity analysis. Based on such analysis, recommendations are given on the most suitable and practical enhancements of the original model. any radius r. The cylinder enclosed within the cover c surrounding the bar is assumed to have n identical and stable cracks that extend radially to a length e. A polar coordinate system is used where the radial and tangential directions are indicated by subscripts r and t, respectively. The hoop (tangential) stress at r = e is equal to the cracking stress ft, and is assumed to vary elastically in the uncracked region, r > e. The model assumes that neighboring longitudinal bars are far enough and that their bond stress fields do not overlap. In the cracked region, r ≤ e, the tangential stress decreases towards the center with the widening of the crack width w until it vanishes at a crack width wc, following a power law as follows, ( ) ( ) 0 1 k c t t w w f w − = σ (1) where k0 = material parameter determined from the tensile fracture energy GF. The hoop strain at r = e, neglecting Poisson’s effect, is obtained from cr c t r E f e ε ε ≡ = ) ( (2) where Ec = concrete modulus of elasticity. This value of the radial strain is assumed constant over the cracked part r ≤ e. Thus, ) ( ) ( 2 ) ( 2 r nw r r e e r r + = ε π ε π , cr r r e r ε ε ε = ≈ ) ( ) ( (3a, b) This yields a linear distribution of crack width, i.e. n r e r w cr ) ( 2 ) ( − = πε for e r ≤ (4) which gives an explicit formula for the hoop stress in the cracked region, namely, ( ) ( ) r w r t σ σ = ) ( for e r rm ≤ ≤ (5) where rm = max {ds / 2, e – wc / 2πεcr } defines the end of the cohesive zone where softening occurs. Given the elastic solution (Timoshenko & Goodier 1951) of stresses at radius r, in a thick-walled cylinder of ri and ro inner and outer radii, respectively, subjected to internal pressure pi, i.e.